In recent years, there have been proposed and developed various automatic lane deviation prevention control technologies. An automatic lane deviation prevention device, capable of executing a lane deviation prevention function, often abbreviated to “LDP function” or a lane deviation avoidance function, often abbreviated to “LDA function”, has been disclosed in Japanese Patent Provisional Publication No. 2000-33860 (hereinafter is referred to as “JP2000-33860”). In the lane deviation prevention (LDP) device disclosed in JP2000-33860, when there is a possibility that a host vehicle deviates from its traffic lane, in order to prevent the host vehicle's deviation from the driving lane, the LDP device controls a braking force of each road wheel depending on a host vehicle's lateral displacement or a host vehicle's lateral deviation from a central axis (a reference axis) of the current driving lane, so that a yawing moment is produced to achieve the host vehicle's return to the reference axis. In such an LDP device as disclosed in JP2000-33860, to avoid the driver from feeling considerable discomfort owing to undesirable fluctuations in the host vehicle's speed, such as rapid vehicle deceleration which may occur during LDP control, a controlled variable of the braking force of each road wheel is generally limited.